10. Case-Control Studies: Odds Ratios, Control Selection, Matching
After this lesson you can
- Define a case-control study by its sampling and draw its schematic with time running the right way
- Explain why the design yields only an odds ratio, and why doubling the controls leaves it unchanged
- Apply the control selection rule and spot a violation, such as clinic controls that turn 3.0 into 1.0
- Compare individual and frequency matching, compute a matched odds ratio from discordant pairs, and recognize overmatching
- State what density sampling does for the odds ratio and name the nested, case-cohort and case-crossover variants
Video coming soon
Scheduled for release on November 7, 2026.
The third of four design lessons, on the study that samples people by outcome and looks back at their exposure. It works one invented study of a rare neurological condition in the fictional Oakhaven Health District, where 75 of 100 cases and 50 of 100 controls were exposed, an odds ratio of 3.0.
Questions and answers
Questions a learner would ask about this lesson. Think through your own answer before you open each one.
- What makes a study a case-control study rather than a retrospective cohort?
Show answer
The sampling variable classifies the design, not the direction of the calendar. A case-control study chooses participants by outcome, people with the condition and comparable people without it, and then looks back at their past exposure. A retrospective cohort chooses people by exposure from old records and then finds their outcomes, even though it also uses the past.
- Why can a case-control study not report a risk or a risk difference?
Show answer
The investigator fixed how many cases and how many controls to enroll, so the table has no population at risk behind its rows. Without a population at risk there is no incidence, so no risk, no rate and no risk difference. The one measure that survives is the odds ratio, read down the columns as exposure odds among cases over exposure odds among controls.
- Why does doubling the number of controls leave the odds ratio unchanged?
Show answer
Controls are a sample of the non-cases in the source population, so each control cell is the true count times one sampling fraction. That fraction appears once on top and once below in the cross-product and cancels. In the Oakhaven example, 200 controls split 100 and 100 still give control exposure odds of 1, so the odds ratio stays 3.0, while the false "risk" across the exposed row halves.
- What is the control selection rule?
Show answer
Controls must come from the same source population as the cases, and they must be chosen independently of exposure. A good control is a person who would have been a case had they developed the condition. In Oakhaven, clinic controls who were often exposed (75 of 100) turned a true odds ratio of 3.0 into 1.0, although nothing about the district had changed.
- What is overmatching, and why should a study never match on the exposure?
Show answer
Overmatching is matching on a variable associated with the exposure but not independently with the condition, or on a variable on the causal path. It makes the exposure odds in the two columns converge, pulls the odds ratio toward 1.0 and creates more concordant pairs that carry no information. Matching on the exposure itself forces equal exposure in cases and controls, so the odds ratio is 1.0 by construction.
Practice quiz
- Question 1Investigators enroll 100 people with a rare condition and 100 without it, then ask about past exposure. What is the design?
- Question 2Cases: 75 exposed and 25 unexposed. Controls: 50 exposed and 50 unexposed. What is the odds ratio?
- Question 3The same study enrolls 200 controls instead of 100, with the same exposure proportion. What happens to the odds ratio?
- Question 4Controls drawn from a clinic whose patients are often exposed to the study exposure violate which principle?
- Question 5In an individually matched study there are 40 discordant pairs in which the case was exposed and the control was not, and 10 in which the control was exposed and the case was not. What is the matched odds ratio?
- Question 6In a matched-pair analysis, which pairs carry no information about the association?
- Question 7Controls are sampled at the times cases occur, from those still at risk. What does the odds ratio then estimate?
- Question 8What is the job of a control group in a case-control study?
- Question 9Which variant draws all cases plus a random subcohort sampled at the start, so the subcohort can serve several outcomes?
- Question 10A district needs an answer this season on many possible exposures for one rare condition with long latency. Which design suits the question best?
Saved in your browser only: no account, no server.
Principles of Epidemiology is education in epidemiologic reasoning, not clinical, screening, or policy guidance. Every example is set in the fictional Oakhaven Health District, and every number is invented for teaching.